naginterfaces.library.tsa.uni_garch_gjr_forecast¶
- naginterfaces.library.tsa.uni_garch_gjr_forecast(nt, ip, iq, theta, gamma, ht, et)[source]¶
uni_garch_gjr_forecast
forecasts the conditional variances, , for from a GJR sequence, where is the forecast horizon and is the current time (see Glosten et al. (1993)).For full information please refer to the NAG Library document for g13ff
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/g13/g13fff.html
- Parameters
- ntint
, the forecast horizon.
- ipint
The number of coefficients, , for .
- iqint
The number of coefficients, , for .
- thetafloat, array-like, shape
The first element must contain the coefficient and the next elements must contain the coefficients , for . The remaining elements must contain the coefficients , for .
- gammafloat
The asymmetry parameter for the sequence.
- htfloat, array-like, shape
The sequence of past conditional variances for the process, , for .
- etfloat, array-like, shape
The sequence of past residuals for the process, , for .
- Returns
- fhtfloat, ndarray, shape
The forecast values of the conditional variance, , for .
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- Notes
In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.
Assume the process can be represented by:
where or , and , if , or , if , has been modelled by
uni_garch_gjr_estim()
, and the estimated conditional variances and residuals are contained in the arrays and respectively.uni_garch_gjr_forecast
will then use the last elements of the arrays and to estimate the conditional variance forecasts, , where and is the forecast horizon.
- References
Bollerslev, T, 1986, Generalised autoregressive conditional heteroskedasticity, Journal of Econometrics (31), 307–327
Engle, R, 1982, Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica (50), 987–1008
Engle, R and Ng, V, 1993, Measuring and testing the impact of news on volatility, Journal of Finance (48), 1749–1777
Glosten, L, Jagannathan, R and Runkle, D, 1993, Relationship between the expected value and the volatility of nominal excess return on stocks, Journal of Finance (48), 1779–1801
Hamilton, J, 1994, Time Series Analysis, Princeton University Press